Question

what is the slope of a line, in the standard (x,y) coordinate plane, that is parallel to 2x + 3y = 12 a. - 3 b. -\frac{2}{3} c. \frac{2}{3} d. \frac{3}{2} e. 3

Explanation:

Step1: Rewrite the equation in slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. We start with the equation $2x+3y = 12$.
Subtract $2x$ from both sides: $3y=-2x + 12$.
Then divide each term by 3: $y=-\frac{2}{3}x + 4$.

Step2: Determine the slope of parallel lines

Parallel lines have the same slope. From the equation $y =-\frac{2}{3}x + 4$, the slope $m$ of the given line is $-\frac{2}{3}$. So a line parallel to it will also have a slope of $-\frac{2}{3}$.

Answer:

b. $-\frac{2}{3}$